Let's chain some tigers now.
I'm not sure if you can chain "square" tigers (where both major diameters are equal). We will use oblong tigers for now.
(sqrt(x^2 + y^2) - 6)^2 + (sqrt(z^2 + w^2) - 3)^2 = 1
(sqrt((x-6)^2 + z^2) - 6)^2 + (sqrt(y^2 + w^2) - 3)^2 = 1
Now, we can have cuts:
X:
(sqrt(a^2 + y^2) - 6)^2 + (sqrt(z^2 + x^2) - 3)^2 = 1
(sqrt((a-6)^2 + z^2) - 6)^2 + (sqrt(y^2 + x^2) - 3)^2 = 1
Y:
(sqrt(x^2 + a^2) - 6)^2 + (sqrt(z^2 + y^2) - 3)^2 = 1
(sqrt((x-6)^2 + z^2) - 6)^2 + (sqrt(a^2 + y^2) - 3)^2 = 1
Z:
(sqrt(x^2 + y^2) - 6)^2 + (sqrt(a^2 + z^2) - 3)^2 = 1
(sqrt((x-6)^2 + a^2) - 6)^2 + (sqrt(y^2 + z^2) - 3)^2 = 1
W:
(sqrt(x^2 + y^2) - 6)^2 + (sqrt(z^2 + a^2) - 3)^2 = 1
(sqrt((x-6)^2 + z^2) - 6)^2 + (sqrt(y^2 + a^2) - 3)^2 = 1
Rotations centered on one tiger (I canceled unit goniometric expressions):
XY:
(sqrt(x^2) - 6)^2 + (sqrt(z^2 + y^2) - 3)^2 = 1
(sqrt((x*cos(a)-6)^2 + z^2) - 6)^2 + (sqrt((x*sin(a))^2 + y^2) - 3)^2 = 1
XZ:
(sqrt((x*cos(a))^2 + y^2) - 6)^2 + (sqrt((x*sin(a))^2 + z^2) - 3)^2 = 1
(sqrt((x*cos(a)-6)^2 + (x*sin(a))^2) - 6)^2 + (sqrt(y^2 + z^2) - 3)^2 = 1
XW:
(sqrt((x*cos(a))^2 + y^2) - 6)^2 + (sqrt(z^2 + (x*sin(a))^2) - 3)^2 = 1
(sqrt((x*cos(a)-6)^2 + z^2) - 6)^2 + (sqrt(y^2 + (x*sin(a))^2) - 3)^2 = 1
YZ:
(sqrt(x^2 + (y*cos(a))^2) - 6)^2 + (sqrt((y*sin(a))^2 + z^2) - 3)^2 = 1
(sqrt((x-6)^2 + (y*sin(a))^2) - 6)^2 + (sqrt((y*cos(a))^2 + z^2) - 3)^2 = 1
YW:
(sqrt(x^2 + (y*cos(a))^2) - 6)^2 + (sqrt(z^2 + (y*sin(a))^2) - 3)^2 = 1
(sqrt((x-6)^2 + z^2) - 6)^2 + (sqrt(y^2) - 3)^2 = 1
ZW:
(sqrt(x^2 + y^2) - 6)^2 + (sqrt(z^2) - 3)^2 = 1
(sqrt((x-6)^2 + (z*cos(a))^2) - 6)^2 + (sqrt(y^2 + (z*sin(a))^2) - 3)^2 = 1
Definitely have a look at these
Rotations centered between tigers:
XY:
(sqrt((x*cos(a)+3)^2 + (x*sin(a))^2) - 6)^2 + (sqrt(z^2 + y^2) - 3)^2 = 1
(sqrt((x*cos(a)-3)^2 + z^2) - 6)^2 + (sqrt((x*sin(a))^2 + y^2) - 3)^2 = 1
XZ:
(sqrt((x*cos(a)+3)^2 + y^2) - 6)^2 + (sqrt((x*sin(a))^2 + z^2) - 3)^2 = 1
(sqrt((x*cos(a)-3)^2 + (x*sin(a))^2) - 6)^2 + (sqrt(y^2 + z^2) - 3)^2 = 1
XW:
(sqrt((x*cos(a)+3)^2 + y^2) - 6)^2 + (sqrt(z^2 + (x*sin(a))^2) - 3)^2 = 1
(sqrt((x*cos(a)-3)^2 + z^2) - 6)^2 + (sqrt(y^2 + (x*sin(a))^2) - 3)^2 = 1
YZ:
(sqrt((x+3)^2 + (y*cos(a))^2) - 6)^2 + (sqrt((y*sin(a))^2 + z^2) - 3)^2 = 1
(sqrt((x-3)^2 + (y*sin(a))^2) - 6)^2 + (sqrt((y*cos(a))^2 + z^2) - 3)^2 = 1
YW:
(sqrt((x+3)^2 + (y*cos(a))^2) - 6)^2 + (sqrt(z^2 + (y*sin(a))^2) - 3)^2 = 1
(sqrt((x-3)^2 + z^2) - 6)^2 + (sqrt(y^2) - 3)^2 = 1
ZW:
(sqrt((x+3)^2 + y^2) - 6)^2 + (sqrt(z^2) - 3)^2 = 1
(sqrt((x-3)^2 + (z*cos(a))^2) - 6)^2 + (sqrt(y^2 + (z*sin(a))^2) - 3)^2 = 1